What does Save As Render do to the image when saving it?
Save as Render will apply the Display Transform set on the Color Management section.





Without the Display Transform the image saved will be saved unprocessed, maintaining the Scene Referred Values, up to the inherent limits of the file format chosen.

For images that require linear values (or non-color-data) leave that box unchecked. (For example when saving normal or depth maps)

Images meant to be saved as Display Referred can be saved as render, so that all color transformations are applied and baked into the picture.

As an example, see how this two images produced with the same scene have different values depending on how they were saved:



There are some notable exceptions to this rule as follows:


The DPX format is unfortunately hard coded to always store a Blender specific transfer curve. It skirts around OCIO in unreliable ways.
The EXR format will always store the internal reference buffer as float or half float. Even with the check box selected, EXRs will not bake any colour transforms, desired or not.
Most other file formats follow the above rule of thumb for display referred formats.